Miller, spray some real thinned Tamiya "buff" over the wheels and lower hull to give it a dusty filthy look. Build it up slowly and then what I do is drybrush the tire color back on the the surface of the tire's where they meet the tracks. That way the sidewalls stay "dirty" looking. If you want darker dirt you could add some dark earth maybe? I used the buff on my marder so not sure on that.
edit: Are you going to use washes and or pastels on it? If so, the wash will also dirty it up and some pastels after the flat coat will too.
Eric